\(a)2018=\left|x-2016\right|+\left|x-2014\right|\)
\(\Rightarrow\hept{\begin{cases}x-2016+x-2014=2018\\x-2016+x-2014=-2018\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}2x-2016-2014=2018\\2x-2016-2014=-2018\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}2x=2018+2016+2014\\2x=-2018+2016+2014\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}2x=6048\\2x=2012\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x=3024\\x=1006\end{cases}}\)
vậy x = 3024 hoặc x = 1006
b) \(\left(x-3\right)^x-\left(x-3\right)^{x+2}=0\)
\(\Rightarrow\left(x-3\right)^x-\left(x-3\right)^x\left(x-3\right)^2=0\)
\(\Rightarrow\left(x-3\right)^x\left[1-\left(x-3\right)^2\right]=0\)
\(\Rightarrow\hept{\begin{cases}\left(x-3\right)^x=0\\1-\left(x-3\right)^2=0\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x-3=0\\\left(x-3\right)^2=1\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x=3\\\left(x-3\right)^2=1\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x=3\\x-3=1\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x=3\\x=4\end{cases}}\)
vậy x = 3 hoặc x = 4
